Quantum Foundations

In this talk, I will demonstrate that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a maximally-entangled state using randomly chosen measurement bases can, with significant probability, generate nonclassical correlations that violate a Bell inequality. For n parties using a Greenberger-Horne-Zeilinger state, this probability of violation rapidly tends to unity as the number of parties increases.

In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded.

For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure.

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.